Re: polredabs(,16)

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Tue, 10 Sep 2002, Igor Schein wrote:
> here's my typical case:
>
> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
> ? \g1
>    debug = 1
> ? polredabs(x^5 - x^4 - 12040781642129393071473904079660253048973811141573673202071693733789883279680587178494462996841316092777725721420479505331283827775*x^3 - 116300336972049690721017379544011576959110565146852966482595449932712559384985831383994266783651912069750389914648201847477549301891914579908523180930736074973601542737568062514475655562681165257*x^2 + 28923689262054691329826006244861882371486999095000166029365674110538452285217184588858628779585349092052020333450432011025074302859688823005297537508940396134093079707594458414327414841760790952734653966377901305736384509781946321196510075808623517993691862754*x + 603824510472333552906408309566519552483702548276229044880954577047602509786254891391799969614095483303548612156918564165324598251084001744566522007323003494588591405487402336312858426924318657537215114711342084660305244042075747811000122705478017654708300091827976086505455932507386781142134969661181915101523617253014533937,16)
[...]
> The polynomial is not reduced, and the only way I know about it is if
> I run at \g, otherwise it's completely silent.  I would like to have
> an option to have
> 62277548538789561520401660217885073427574453048708934544094318214969928190701341602751
> from the example above factored:
>
> ? factor(62277548538789561520401660217885073427574453048708934544094318214969928190701341602751)
>
> [524351 15]
>
> So basically, leave polredabs(,16) behave as it does now, and have,
> say, polredabs(,24) factor JUST the composites that appear in
> impossible inverse.

Not necessary. It was a bug in allbase(), introduced by my recent patch [ try
to recover when exception "impossible inverse mod..." is raised ]. It is
allowed to have pseudoprimes in the discriminant factorization, but it is
crucial that these be coprime !

I have modified the recovery code to enforce this (thereby discovering new
factors, and reducing the number of failures). Does any of your examples
break it ?

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
Dép. de Mathematiques, Bat. 425  Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
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